The archbishop of Canterbury, Dr Rowan Williams, in York Minster. Photograph: John Giles/PA

A potentially historic vote on legislation to allow women to become bishops appeared increasingly likely to be postponed as the archbishop of Canterbury acknowledged that the Church of England had "backed itself" into a corner over the long-running and divisive issue.

In a indication of growing concern among senior church officials responsible for drawing up the measure, the steering committee for the legislation announced it would seek to have Monday's debate adjourned to allow a chastened House of Bishops to reconsider a last-ditch amendment that has sparked fury from many female clergy.

If voted through by the General Synod, which is meeting in York, the adjournment would result in the legislation being re-examined in September and returning in revised form in November. Many campaigners for women bishops, who insist the amendment in question is offensively discriminatory, would breathe a huge sigh of relief.

The issue, which has been 12 tortuous years in the making, has pitted a growing number of supporters against a stubborn minority of Christians who, as either traditionalist Anglo-Catholics or conservative evangelicals, refuse to countenance the idea of women bishops.

Rowan Williams said on Sunday the church had got itself into a tricky position over the issue. "It is a corner into which the church has backed itself and out of which we are trying to get." he said.

Earlier, during a sermon at York Minster, he warned those assembled against becoming consumed by the row and encouraged them to overcome differences.

"Many of us in the church are feeling profoundly frustrated," he said, adding later: "Most of us are frustrated with the structures of the church and are feeling that the way in which we are doing our business is at the moment preventing us from doing what we actually want to do as a church."

Many, he added, were frustrated with the bishops, who have been accused by some campaigners and clergy of having "meddled" with a piece of draft legislation that had already met with the approval of 42 of 44 dioceses.

Williams, who said on Friday he "longed" to see women bishops, warned against letting the increasingly fraught debate send the church into depression. "The last thing our society or our world needs is a depressed church," he said. "That is something I hope we shall bear in mind and heart in the days ahead."

There is a growing concern among supporters of women bishops that the longer the debate drags on, the more old-fashioned the Church will appear to the general public. According to a ComRes poll commissioned by the Bible Society and released today, 73% of people think the church is "out of touch" with modern society's view of women. Rowan Williams said: "this is very saddening".

Three-quarters of respondents - 74% - said they thought the Church should allow women to be bishops.

If the debate is adjourned and revised legislation returns to the Synod in November, women could still theoretically be consecrated by 2014. If it is not adjourned and the measure is voted through with a two-thirds majority, they could even enter the episcopate by the end of next year – but on the basis of legislation despised by many senior women clergy. If the measure is put to the vote and fails, the legislation will be shelved until 2015.